Well-defined forward operators in dynamic diffractive tensor tomography using viscosity solutions of transport equations
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Publication:2079460
DOI10.1553/etna_vol57s80zbMath1498.35631arXiv2111.05722OpenAlexW3213065486MaRDI QIDQ2079460
Publication date: 30 September 2022
Published in: ETNA. Electronic Transactions on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2111.05722
geodesicstransport equationviscosity solutionsattenuated refractive dynamic ray transform of tensor fields
Inverse problems for PDEs (35R30) Initial value problems for linear first-order PDEs (35F10) Inverse problems for integral equations (45Q05) Viscosity solutions to PDEs (35D40) PDEs on manifolds (35R01) Initial-boundary value problems for linear first-order PDEs (35F16) Transport equations (35Q49)
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Cites Work
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- Inverting the local geodesic X-ray transform on tensors
- Stability estimates for the \(X\)-ray transform of tensor fields and boundary rigidity
- The attenuated ray transform for connections and Higgs fields
- An abstract framework for parabolic PDEs on evolving spaces
- Two dimensional compact simple Riemannian manifolds are boundary distance rigid
- Inversion of the Attenuated Geodesic X-Ray Transform over Functions and Vector Fields on Simple Surfaces
- An iterative method to reconstruct the refractive index of a medium from time-of-flight measurements
- On the inversion formulas of Pestov and Uhlmann for the geodesic ray transform
- Numerical Implementation of Geodesic X-Ray Transforms and Their Inversion
- Rigidity of broken geodesic flow and inverse problems
- User’s guide to viscosity solutions of second order partial differential equations
- Influence of refraction to the accuracy of a solution for the 2D-emission tomography problem
- Efficient algorithms for the regularization of dynamic inverse problems: I. Theory
- Efficient algorithms for the regularization of dynamic inverse problems: II. Applications
- The attenuated geodesic x-ray transform
- A motion artefact study and locally deforming objects in computerized tomography
- Differential Equations and Uniqueness Theorems for the Generalized Attenuated Ray Transforms of Tensor Fields
- Inverse problems with inexact forward operator: iterative regularization and application in dynamic imaging
- Diffraction tomography of strain
- The method of the approximate inverse for atmospheric tomography
- Efficient algorithms for linear dynamic inverse problems with known motion
- Slice-by-slice reconstruction algorithm for vector tomography with incomplete data
- ON A „MONOTONICITY” METHOD FOR THE SOLUTION OF NONLINEAR EQUATIONS IN BANACH SPACES
- Singular value decomposition and its application to numerical inversion for ray transforms in 2D vector tomography
- Some Properties of the Eigenfunctions of The Laplace-Operator on Riemannian Manifolds
- Nonlinear partial differential equations with applications
- Integral geometry of a tensor field on a manifold whose curvature is bounded above
